Information entropy, as a quantitative measure of complexity in nonlinear systems, has been widely researched in a variety of contexts. With the development of a nonlinear dynamic, the entropy is faced with severe challenges in dealing with those signals exhibiting extreme volatility. In order to address this problem of weighted permutation entropy, which may result in the inaccurate estimation of extreme volatility, we propose a rescaled range permutation entropy, which selects the ratio of range and standard deviation as the weight of different fragments in the time series, thereby effectively extracting the maximum volatility. By analyzing typical nonlinear systems, we investigate the sensitivities of four methods in chaotic time series where extreme volatility occurs. Compared with sample entropy, fuzzy entropy, and weighted permutation entropy, this rescaled range permutation entropy leads to a significant discernibility, which provides a new method for distinguishing the c...

中文翻译：

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重标范围置换熵：一种量化混沌时间序列中极度波动动态复杂度的方法

信息熵作为非线性系统中复杂性的定量度量，已经在各种情况下得到了广泛的研究。随着非线性动力学的发展，在处理那些表现出极大波动性的信号时，熵面临着严峻的挑战。为了解决加权置换熵的问题，该问题可能导致对极端波动率的不正确估算，我们提出了一种重新定标的距离置换熵，该​​熵选择距离与标准偏差之比作为时间序列中不同片段的权重，从而有效地提取最大波动率。通过分析典型的非线性系统，我们研究了出现剧烈波动的混沌时间序列中四种方法的灵敏度。与样本熵，模糊熵相比，